The article is also currently on the newsstands/bookstores (through late March 2010) in DISCOVER Magazine's "Extreme Universe" special issue.

There are actually people trying to make that happen. They claim they need 5 years given the engineering challenges. The article was written in 2005. It is now 2010, so .....

Well? Where are we?

I can help, because I'm aware of the challenges (making the apparatus as vibration-free as possible, with constant temperature in a wind-free environment). I've worked on a Mach-Zehnder Interferometer with the necessary lasers, mirrors, beam-splitters, concrete floor, balloon tires, in a quiet, dark air-tight lab in a high-vacuum environment, etc.

I'd like to put my Mechanical Engineering knowledge AND experience to good use. If anyone knows who is currently doing these tests, please forward this webpage to them. Thanks in advance.

Friday, January 29, 2010

Interestingly, if Hořava-Lifshitz gravity is combined with Kaluza-Colyer 5-D(4S+1T) Toroidal-Cylinder Theory, all the problems of particle physics are solved, including the masses of the fundamentals and Dark Energy and Dark Matter as well (they're geometrical, as expected).

LOL, no they're not. But only because I haven't fully explored Kaluza-Colyer theory! :-)

Thursday, January 28, 2010

Note to The Royal Swedish Academy: Although the following people are quite dead, we your adoring public, and in great appreciation of the great man that Alfred Nobel was and in your good service thereof, and in great respect to his Last Will and Testament and the intent of his Prizes, humbly request you extend tradition and give post-humous Nobel Prizes in Physics to the following people for their extraordinary accomplishments in Physics:

- Nikola Tesla, of Austrian Empire/United States, and Thomas Edison, of United States, for multiple contributions in Electromagnetism

- Lise Meitner, of Austria/Sweden and Fritz Strassmann, of Germany, for contributions to nuclear fission

- Albert Einstein, of Germany/Switzerland/United States, for The Special Theory of Relativity

- Albert Einstein, of Germany/Switzerland/United States, for The General Theory of Relativity

Einstein already won for the Photoelectric Effect, but most would agree he deserved 5 more.

- Wolfgang Pauli, of Austria/United States, for Neutrinos

Pauli already won for his Exclusion Principle which launched Chemistry into the stratosphere, but he deserves another in our humble opinion

- Chung-Yao Chao, of China, for experiments leading to the recognition of the positron

- Boris Poldolsky, of Russia/United States, for EPR

- Nathan Rosen, of United States/Israel, for EPR

- Cesar Lattes, of Brazil, and Eugene Gardner, of United States, for discoveries regarding the pion for which their boss Cecil Powell won the award

- Julius Edgar Lilienfeld, of Austria/United States, and Oskar Heil of Germany/United States, for the groundwork that led to the invention of the transistor

- Chien-Shiung Wu, of China/United States, for disproving the law of conservation of parity and numerous contributions
- Ennackal Chandy George Sudarshan, of India/United States, and Robbert Marshak, of United States, for the V-A Theory of Weak Interactions (Sudershan is still alive)

- Ennackal Chandy George Sudarshan, of India/United States, for the Sudarshan diagonal representation (also known as Sudarshan-Glauber representation ) in quantum optics (Sudershan is still alive)

George Sudarshan currently holds the record of the most nominated Nobel Prize candidate alive who has yet to receive any Nobel Prize

- Yuval Ne'eman, of Israel, for his 1961 discovery of the classification of hadrons through the SU(3) flavour symmetry

- Jocelyn Bell Burnell, of United Kingdom, who discovered the first radio pulsars, with her thesis supervisor Antony Hewish, for which Hewish shared the NPP with Martin Ryle.

In more sobering news, I just found out that noted Cosmologist Andrew Lange of CalTech took his own life, at the far too young age of 53 (my age). Click on the following link for details of the sad news: Andrew Lange (1956-2010)

I'm zeroing in on that which I wish to specialize in for the next 22 years before the synapses in my brain begin to widen and dementia begins. Since I've narrowed my search down to Nonlinear Dynamics, check, with N=Continuum, check, this is the first of several candidates:

SOLITONS

From Wikipedia, the free encyclopedia

In mathematics and physics, a soliton is a self-reinforcing solitary wave (a wave packet or pulse) that maintains its shape while it travels at constant speed. Solitons are caused by a cancellation of nonlinear and dispersive effects in the medium. (The term "dispersive effects" refers to a property of certain systems where the speed of the waves varies according to frequency.) Solitons arise as the solutions of a widespread class of weakly nonlinear dispersive partial differential equations describing physical systems. The soliton phenomenon was first described by John Scott Russell (1808–1882) who observed a solitary wave in the Union Canal in Scotland. He reproduced the phenomenon in a wave tank and named it the "Wave of Translation".

Contents

Definition

A single, consensus definition of a soliton is difficult to find. Drazin and Johnson (1989) ascribe 3 properties to solitons:[1]

They are of permanent form;

They are localised within a region;

They can interact with other solitons, and emerge from the collision unchanged, except for a phase shift.

More formal definitions exist, but they require substantial mathematics. Moreover, some scientists use the term soliton for phenomena that do not quite have these three properties (for instance, the 'light bullets' of nonlinear optics are often called solitons despite losing energy during interaction).

History

In 1834, John Scott Russell describes his wave of translation.[nb 1] The discovery is described here in Scott Russell's own words:[nb 2]"I was observing the motion of a boat which was rapidly drawn along a narrow channel by a pair of horses, when the boat suddenly stopped – not so the mass of water in the channel which it had put in motion; it accumulated round the prow of the vessel in a state of violent agitation, then suddenly leaving it behind, rolled forward with great velocity, assuming the form of a large solitary elevation, a rounded, smooth and well-defined heap of water, which continued its course along the channel apparently without change of form or diminution of speed. I followed it on horseback, and overtook it still rolling on at a rate of some eight or nine miles an hour, preserving its original figure some thirty feet long and a foot to a foot and a half in height. Its height gradually diminished, and after a chase of one or two miles I lost it in the windings of the channel. Such, in the month of August 1834, was my first chance interview with that singular and beautiful phenomenon which I have called the Wave of Translation".[2]
Scott Russell spent some time making practical and theoretical investigations of these waves. He built wave tanks at his home and noticed some key properties:

The waves are stable, and can travel over very large distances (normal waves would tend to either flatten out, or steepen and topple over)

The speed depends on the size of the wave, and its width on the depth of water.

Unlike normal waves they will never merge – so a small wave is overtaken by a large one, rather than the two combining.

If a wave is too big for the depth of water, it splits into two, one big and one small.

Solitons in fiber optics

Much experimentation has been done using solitons in fiber optics applications. Solitons' inherent stability make long-distance transmission possible without the use of repeaters, and could potentially double transmission capacity as well.[4]
In 1973, Akira Hasegawa of AT&TBell Labs was the first to suggest that solitons could exist in optical fibers, due to a balance between self-phase modulation and anomalous dispersion. Also in 1973 Robin Bullough made the first mathematical report of the existence of optical solitons. He also proposed the idea of a soliton-based transmission system to increase performance of optical telecommunications.
Solitons in a fiber optic system are described by the Manakov equations.
In 1987, P. Emplit, J.P. Hamaide, F. Reynaud, C. Froehly and A. Barthelemy, from the Universities of Brussels and Limoges, made the first experimental observation of the propagation of a dark soliton, in an optical fiber.
In 1988, Linn Mollenauer and his team transmitted soliton pulses over 4,000 kilometers using a phenomenon called the Raman effect, named for the Indian scientist Sir C. V. Raman who first described it in the 1920s, to provide optical gain in the fiber.
In 1991, a Bell Labs research team transmitted solitons error-free at 2.5 gigabits per second over more than 14,000 kilometers, using erbium optical fiber amplifiers (spliced-in segments of optical fiber containing the rare earth element erbium). Pump lasers, coupled to the optical amplifiers, activate the erbium, which energizes the light pulses.
In 1998, Thierry Georges and his team at France Telecom R&D Center, combining optical solitons of different wavelengths (wavelength division multiplexing), demonstrated a data transmission of 1 terabit per second (1,000,000,000,000 units of information per second).
For some reasons, it is possible to observe both positive and negative solitons in optic fibre. However, usually only positive solitons are observed for water waves since any attempt to create a wave of depression results in a train of oscillatory waves. (A positive soliton is related to a positive sech2 profile and a negative soliton is connected to a wave profile of the form −sech2.)
In 2000, Cundiff predicted the existence of a vector soliton in a birefringence fiber cavity passively mode locking through SESAM. The polarization state of such a vector soliton could either be rotating or locked depending on the cavity parameters.[5]
In 2008, D.Y.Tang et al. observed a novel form of higher-order vector soliton from the perspect of experiments and numerical simulations. Different types of vector solitons and the polarization state of vector solitons have been investigated by his group.[6]

Bions

The bound state of two solitons is known as a bion.
In field theory Bion usually refers to the solution of the Born–Infeld model. The name appears to have been coined by G.W. Gibbons in order to distinguish this solution from the conventional soliton, understood as a regular, finite-energy (and usually stable) solution of a differential equation describing some physical system.[8] The word regular means a smooth solution carrying no sources at all. However, the solution of the Born-Infeld model still carries a source in the form of a Dirac-delta function at the origin. As a consequence it displays a singularity in this point (although the electric field is everywhere regular). In some physical contexts (for instance string theory) this feature can be important, which motivated the introduction of a special name for this class of solitons.
On the other hand, when gravity is added (i.e. when considering the coupling of the Born–Infeld model to General Relativity) the corresponding solution is called EBIon, where "E" stands for "Einstein".

Notes

^ "Translation" here means that there is real mass transport, although it is not the same water which is transported from one end of the canal to the other end by this "Wave of Translation". Rather, a fluid parcel acquires momentum during the passage of the solitary wave, and comes to rest again after the passage of the wave. But the fluid parcel has been displaced substantially forward during the process – by Stokes drift in the wave propagation direction. And a net mass transport is the result. Usually there is little mass transport from one side to another side for ordinary waves.

^ This passage has been repeated in many papers and books on soliton theory.

^Lord Rayleigh published a paper in Philosophical Magazine in 1876 to support John Scott Russell's experimental observation with his mathematical theory. In his 1876 paper, Lord Rayleigh mentioned Scott Russell's name and also admitted that the first theoretical treatment was by Joseph Valentin Boussinesq in 1871. Joseph Boussinesq mentioned Russell's name in his 1871 paper. Thus Scott Russell's observations on solitons were accepted as true by some prominent scientists within his own life time of 1808–1882.

^ Korteweg and de Vries did not mention John Scott Russell's name at all in their 1895 paper but they did quote Boussinesq's paper of 1871 and Lord Rayleigh's paper of 1876. The paper by Korteweg and de Vries in 1895 was not the first theoretical treatment of this subject but it was a very important milestone in the history of the development of soliton theory.

Sunday, January 24, 2010

From Albert Einstein's notebooks, on a sweet spring day in the early days of The Institute for Advanced Study at Fine Hall in Princeton once upon a time, on his attempt to solve The Three-body Problem:*

* - OK, I lied, sorry. That is NOT from Einstein's notebooks. I don't know where it's from, but it's funny. :-)

No need to explore three bodies for the moment though. The two body problem is easier, is linear, and here's a sweet application by Strogatz:

First, click here to see a New York Times guest columnist piece by Stephen Strogatz on Romeo-and-Juliet Mathematics. The replies are pretty funny. :-)

A first order system of equations to model the evolution in time of the relationship can be written as (Rdot = dR/dt = rate of change of R, and similarly for Jdot):

Rdot = a R + b J

Jdot = c R + d J

where a,b,c,d are parameters which can be positive, negative or zero, with the following "meanings":

a and d: "cautiousness" (throw towards (if a,d>0) the other or avoid (if a,d<0) the other)

b and c: "responsiveness" (degree at which they react to the other's advances)

For instance a case where Romeo has both a>0 and b>0 can be called an "eager beaver" (he gets excited by Juliet's love and is further excited by his own feelings into a "snowball of affection").

But if a<0 and b>0 ("cautious lover"), it means that the more Romeo loves Juliet (R>0), the more he wants to "run away" from her (Rdot more negative, particularly acute near marriage decisions...); and the more he hates her (R<0) the more he increases his love (Rdot more positive, nothing like distance to inflame his fellings).

If a<0 and b<0 ("cautious and unresponsive") usually not a good chance for romance, "lets just be friends" type...

If a>0 and b<0 ("daring but unresponsive") is more the "narcisist" type...

Typical issues of these "dynamical love systems" is which relationships are "viable"...

Notice that the "fixed points", that is where the system will stabilize would be given by

Rdot=0

Jdot=0

that is :

a R + b J =0

c R + d J =0

which is a system of two algebraic equations with two unknowns (R and J).

Let's analyze some special cases:

1) Two identical cautious lovers: a=d<0 , b=c>0
Then det=ad-bc=a2 -b2 , and the solutions behave in the following way:

i) If a2>b2 the lovers are more cautious than "responsive" and the relationship "fizzles out " to mutual indifference R=J=0 (caution leads to apathy)

ii) If a22) Out of touch with their own feelings: a=0, d=0 (lovers only react to the others feelings)

Then det=ad-bc=-bc, and the equations are:

Rdot = b J

Jdot = c R

Find out what happens!3) Do opposites attract? Analyze d=-a, c=-b.4) Do identical lovers make for good couples? d=a, c=b5) Analyze your own "made up" case of interest!

Here's what interests me, the Eurorock band "T'Pau" performing their 1987 hit, "Heart and Soul":

Click here to see a highly interactive version of Brian Castellani's Complexity Map, as shown below:

VI. Personal History

I'm as happy as a Philosophy Grad Student at the beginning of his first lecture of his first teaching job teaching "Introduction to Plato". *

Why?

Because, I've finally found my specialty, thanks to United Parcel Service delivering the following book from Amazon to my doorstep yesterday:

By the way, I really hate, loathe and despise the term "Chaos Theory." The proper description would be "Structure-in-Chaos" Theory. It's young, it's happening, it's taking off in many different fields, and the high-speed computers of Computer Scientists and their wonderful Algorithms are its very best friend. We have miles to go before we sleep. Time to get cracking! :-)

From Wikipedia, at which an input of "Nonlinear Dynamics" directs to "Nonlinear differential equations" under "Nonlinear systems." Under that section it states:

A system of differential equations is said to be nonlinear if it is not a linear system. Problems involving nonlinear differential equations are extremely diverse, and methods of solution or analysis are problem dependent. Examples of nonlinear differential equations are the Navier–Stokes equations in fluid dynamics, the Lotka–Volterra equations in biology, and the Black–Scholes PDE in finance.
One of the greatest difficulties of nonlinear problems is that it is not generally possible to combine known solutions into new solutions. In linear problems, for example, a family of linearly independent solutions can be used to construct general solutions through the superposition principle. A good example of this is one-dimensional heat transport with Dirichlet boundary conditions, the solution of which can be written as a time-dependent linear combination of sinusoids of differing frequencies; this makes solutions very flexible. It is often possible to find several very specific solutions to nonlinear equations, however the lack of a superposition principle prevents the construction of new solutions.

Going to the top of the page:

In mathematics, a nonlinear system is a system which is not linear, that is, a system which does not satisfy the superposition principle, or whose output is not proportional to its input. Less technically, a nonlinear system is any problem where the variable(s) to be solved for cannot be written as a linear combination of independent components. A nonhomogeneous system, which is linear apart from the presence of a function of the independent variables, is nonlinear according to a strict definition, but such systems are usually studied alongside linear systems, because they can be transformed to a linear system of multiple variables.
Nonlinear problems are of interest to physicists and mathematicians because most physical systems are inherently nonlinear in nature. Nonlinear equations are difficult to solve and give rise to interesting phenomena such as chaos. The weather is famously nonlinear, where simple changes in one part of the system produce complex effects throughout.

And that's it for today. For all my regular readers (all 4 of you ... it would be 5 but Mom passed away in 2008) I'm afraid I will spend less time on-line and at this blog, as I have much to read. I won't go away completely, but for the most part I'll be incognito. Cheers and farewell, and here's hoping I do Mom proud, wherever she is, when I publish my first paper in 6 months to 3 years, or so.

* - most of whom start off with: "I am SO ENVIOUS of you people! You are about to hear about Plato for the FIRST time!" They have their point.

Sincerely,
S'Colyer

P.S. For your viewing and listening pleasure (subjective), a VERY non-linear song:

Here is the Number One most popular song in America today, Empire State of Mind by Jay-Z and Alicia Keys. Keys' bits are beautifully linear, Jay-Z's nonlinear. Somehow, they blend well:

Monday, January 18, 2010

"Hammock Physicist" Johannes Koelman has made a bold statement at his blog regarding the title of this blarticle, which I strongly recommend we read then examine by clicking here. Read the replies as well, as they're also interesting and no less important.

Essentially, the bulk of Koelman's work is as follows, and in his words from his article:

I previously posed the question “can dark energy, just like gravity, be understood as an entropic effect?”.

To my astonishment, it appears that a quick 10 minute exercise in determining the entropic force exerted on the entire observable universe indeed yields an effect with the right order of magnitude to explain the cosmic dark energy (or cosmic acceleration). It seems that a dark energy effect emerges from Verlinde's holographic description. All 123 orders of magnitude of the dark energy mismatch evaporate when considering the cosmic acceleration as a result of a holographic entropic force.

The line of reasoning is as follows (for ease of notation I will work in natural units and leave out factors c, G and h-bar):

1. Consider the cosmic horizon (the edge of the observable universe: a sphere with radius R approximately equal to 2.7 10^61 in natural units)

2. According to the holographic principle the observable universe is encoded in N = pi R^2 bits located at the cosmic horizon,

3. A finite temperature T is associated with this horizon. This temperature is determined by an equipartition of the energy Mc^2 contained within the horizon over the bits (degrees of freedom) associated with the horizon. Here M = 1.4 10^60 is the observable mass of the universe. Using the equipartition expression ½kT = M/piR^2, it follows that kT = 3 10^-64.

Two critical notes to the above speculative derivation need to be mentioned here:

1. As I set out to explain more than a hundred orders of magnitude mismatch, I have not bothered myself with numerical factors of order unity. As a result,the end result could be off by a factor of two or so.

2. More importantly, a full evaluation of the above simple expansion model yields an expansion (1/R)d^2R/dt^2 = (2c/R)^2. Whilst this expression yields the right order of magnitude for the expansion, it is not constant and therefore not in line with the full Lambda-CDM model cosmological model. Is it a coincidence that the current value of the dark energy density comes out right? Or does the Lambda-CDM model need a modification?

You can read about it in the Science News article I came across today: here.

DARK MATTER has yet to be proven, and the competing theory of MOND/TeVeS in which Newton's equations (particularly F=ma) are modified and "Dark Matter" "particles" are unnecessary, has yet to be falsified, yet it gets little to no attention, in comparison.

Mordehai Milgrom is THE guy in MOND. Here is his picture:

Read all about Mordehai Milgrom and the MOND/TeVeS vs Dark Matter controversy: here.

"Historically, the greatest difficulty in scientific revolutions is usually not the missing piece but the extraneous one - the assumption that we've all taken for granted but is actually unnecessary. Philosophers are trained to smoke out these mental interlopers. Many of the problems that scientists now face are simply the latest guise of deep questions that have troubled thinkers for thousands of years. Philosophers bring this depth of experience with them. Many have backgrounds in physics as well."
.....George Musser, Scientific American Senior Editor

I. Time
II. Gravity
III. In Conclusion

I. TIME

Time. It's a Dimension. It's the 4th of the 4 dimensions we know of. It's also the strangest of them all, due to its apparent uni-directionality. Entropy and The Second Law of Thermodynamics seem to be involved.

First up, Richard Feynman's lecture at Cornell:

And then there's this, by Science Comedian Brian Malow :

"If we are considering the fundamental level of reality, and asking the most fundamental questions about dynamics, we come up against the question “What decides how things change?” At this fundamental level, the physical laws can seem somewhat arbitrary (for example, the amount of charge on an electron). In fact, at this most fundamental level, the only principle which seems likely to describe dynamics seems to come from mathematics not physics: a system will have many more possible disordered states than ordered states, so a system which changes state randomly will most likely move to a more disordered state.

"While the second “law” of thermodynamics is “just” a statistical principle, it is a mightily powerful statistical principle! This is because the basis of the second law – that “disorder will increase” – seems so obvious, and seems to appeal to a fundamental, platonic principle of mathematics. For this reason, the second law manages to appear even more fundamental and unbreakable than the other physical laws, which seem rather arbitrary in comparison. Hence Arthur Eddington’s famous quote: “If someone points out to you that your pet theory of the universe is in disagreement with Maxwell’s equations – then so much the worse for Maxwell’s equations. If it is found to be contradicted by observation – well, these experimentalists do bungle things sometimes. But if your theory is found to be against the second law of thermodynamics I can offer you no hope; there is nothing for it but to collapse in deepest humiliation.”

Gravity. It's a Force. It's the force we've known about the longest, yet, the one we seem to know the least about. It's the strangest of them all due to its weakness, and its range.

Interestingly, Lubos Motl has a blarticle up about Gravity. It's interesting to me because for the first time in a long time, Lubos is actually UNdecided about something ... for a change. The title of the blarticle is "Gravity as a Holographic Entropic Force", and the replies are no less important than Lubos' excellent blarticle. Click here and read it. It won't be "time" wasted, heh.

It refers to U. Amsterdam's Erik Verlinde's January 6, 2010 paper, here, titled On the Origin of Gravity and the Laws of Newton.

UPDATE (Jan.11): Peter Woit notes Verlinde's paper along with Sean Carroll's new book and something called "The Entropic Landscape" at "Not Even Wrong" in the blarticle "The Entropy Decade", here.

UPDATE (Jan. 12): Erik Verlinde has received criticism, and defends himself today: here.

UPDATE ( Jan. 14): Verlinde defends himself at Lubos Motl's The Reference Frame: here. It's worth reading the comments section as Lubos finds this new way of looking at things both interesting and vexing.

UPDATE (Jan. 17) - "The Hammock Physicist's" Johannes Koelman's Blog has a very nice History of Verlinde's work spread over 3 articles in Dec. '09 and Jan. '10, which should be read in the following order, including the replies. They are:
1) Dec. 14 - "Holographic Hot Horizons" - Click here.
2) Dec. 17 - "Holographic Horizons Get Hotter" - Click here.
3) Jan. 7 - "It From Bit: The Case of Gravity" - Click here.
They should be read in order, but the replies to 2) above are very interesting, in which Sunu Engineer (not verified) claims Verlinde's work has already been done by another Scientist named Thanu Panmanabhan. It's a bit messy, but their two approaches are different. I don't get into political sparring among scientists. The gossips love it but I find it messy and embarrassing.

Speculative Physicists are falling all over themselves in trying to describe "Time" and "Gravity", sometimes together, but eventually they fall back into Philosophy in trying to defend (cough) excuse me, I meant describe their own individual takes on this stuff.

So my question is, are there any TRUE Philosophers out there who care to weigh in?

Remember, the purpose of Philosophy is to challenge not the math so much, but the ASSUMPTIONS. George Musser taught me that.

So, Philosophers, I ask you ...

Is Time REALLY a Dimension? Or is it something else? A partial Dimension? An illusion? An absolute value or an ever changing thing?

Is Gravity REALLY a Force? Or is it something else? Simple geometry? An illusion, being the reflection of a true force on a supra-dimensional plane? Since it seems to be tied to mass, what is mass, exactly?

I understand all sorts of mathematics work out splendidly when Time is treated as a Dimension and Gravity as a Force, and it is not my intention to get into semantic arguments. I'm just asking.

IV. MUSIC (Ice for the overheated brain)

Music to contemplate by (from "The Continuing Adventures of Paul on the Floor" by Johnny and the Moondogs, at the first ever outdoor stadium concert way back in 1965):

Finally, Ringo requests more Feynman. Here you go, Ringo:

Finally, in my Philosopher buddy Phil Warnell's (see relies below) honor, here is one of the most haunting songs of the 1960's, from a singing duo that rivaled The Beatles in their day. The music is beautiful, it's the lyrics that haunt. They remind me of Paul Dirac, and David Deustch, and ... me. In my (early) teenage years, anyway.

Art Garfunkel (the guy on the right) got his Masters Degree in Mathematics. He was set to go for his PhD., when destiny (Stardom) called.

Finally, and in great honor to my dear friend Andrew Thomas of Swansea, Wales, UK, who saved me from ditching Mathematical Physics entirely, and at the very last moment before I would have done so, thanks to his GREAT Indroduction to Quantum Mechnics website "What is Reality?", and who furthermore doesn't appreciate The Beatles as much as he should, yet DOES appreciate that great "unifier" of Elvis, Beatles and Motown that is Michael Jackson ... I give my personally favorite video of MJ's, the wonderful "Black or White",

About Me

My weblog is named "Multiplication by Infinity", because "Division by Zero" was taken ... and "Division by Infinity" makes me feel very small ... Steven Colyer's Musings in Mathematical Physics and its Effects on Humanity and other Lifeforms.... And Pure Mathematics, Computer Science, Applied Mathematics, Experimental Physics, Engineering, Astronomy (not Cosmology so much), Space Exploration and Lunar Colonization.
I am a Rutgers 1979 Mechanical Engineer (Pi Tau Sigma) and Rutgers 1989 MBA.
("I study Politics and War that my children may study Mathematics and Philosophy."
- 2nd U.S. President John Adams)
I've already studied enough Politics and War and Economics for one lifetime, and so it's time for Math and Science